Major League Baseball now records information about every pitch
thrown in every game of every season. Statistician Jim Albert
compiled data about every pitch thrown by 20 starting pitchers
during the 2009 MLB season. The data set included the type of pitch
thrown (curveball, changeup, slider, etc.) as well as the speed of
the ball as it left the pitcher’s hand. A histogram of speeds for
all 30,740 four-seam fastballs thrown by these pitchers during the
2009 season is shown below, from which we can see that the speeds
of these fastballs follow a Normal model with mean μ = 92.12 mph
and a standard deviation of σ = 2.43 mph.
A)Compute the z-score of pitch with speed 89.9 mph. (Round your answer to two decimal places.)
B)Approximately what fraction of these four-seam fastballs would you expect to have speeds between 86.5 mph and 93.7 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.)
C)Approximately what fraction of these four-seam fastballs would you expect to have speeds above 93.7 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.)
D)A baseball fan wishes to identify the four-seam fastballs among the slowest 2% of all such pitches. Below what speed must a four-seam fastball be in order to be included in the slowest 2%? (Round your answer to the nearest 0.1 mph.)
Major League Baseball now records information about every pitch thrown in every game of every season....
Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher’s hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown...
Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher's hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown...
Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher's hand. A histogram of speeds for all 30,740 four seam fastballs thrown by these pitchers during the 2009 season is...